How to soften/smooth mesh curves?
You probably don't need all those subdivisions on the edges that run across the curve:



Aside from that, there are several ways you could go about doing this:
Spin
You could use the spin tool (⎇ AltR):

Position the 3D cursor ( LMB)

Spin (⎇ AltR)




Subdivide
Subdividing can work well if you only subdivide the edges that follow around the curve:

Unfortunately subdivide smooth doesn't seem to work in this case, so you'll still need to move the vertices manually.
Curves
You could also use a curve, then convert it to a mesh later with ⎇ AltC.

Add a curve

Add a straight curve as a bevel object

Extrude curve (E or ⎈ Ctrl LMB)




You should also be able to use bevel, but currently there seems to be a bug with beveling 2D planes in 2.72..